Let X have the density friction f(x) = 2 X (1 - x) lt is know that 1/4 of all fa

Question

Let X have the density friction f(x) = 2 X (1 - x) lt is know that 1/4 of all families living in Baltimore have annual income exceeding $20.000, what is the probability that at least 3 families among 4 randomly chosen will have annual income below $20.000. Find Z if the probability that a random variable hating the standard normal distribution will take on a Value greater than Z is 0.8062 If X is a normal random variable with mean 80 and standard deviation 10. compute the following probabilities, (a) p (x lessthanorequalto 100) (b) p (85 lessthanorequalto x lessthanorequalto 95)

Explanation / Answer

7)f(x) =(2x-2x2)

a) mean =E(X) = xf(X) dx = (2x2-2x3) dx =(2x3/3-2x4/4)|10 =0.1667

E(X2)== x2f(X) dx = (2x3-2x4) dx =(2x4/4-2x5/5)|10 =0.1

b)hence variance(X) =E(X2)-(E(X))2 =0.0722

c)E(9X+3X2)=9*0.1667+3*0.1=1.8003

8) P(X>=3)=34 4Cx (0.75)x(0.25)4-x =0.7383

9)P(Z>Z)=0.8962

z=-1.2602

10)P(X<100)=P(Z<2)=0.97725

P(85<X<95)=P(0.5<Z<1.5)=0.9332-0.6915=0.2417

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